Finite Group Databasebeta

← C11×#24531 #14601724

Subgroups — C11×#24531 #14601724

Order 2816.

1224 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#447C211yesmaximal, characteristic
2C22×C11×#102C211yesmaximal, characteristic, complemented
3C11×#2504C211yesmaximal, characteristic, complemented
4D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#2073C212yesmaximal, complemented
6C11×#2054C212yesmaximal, complemented
7C11×#1893C211yesmaximal, characteristic, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1824C211yesmaximal, characteristic, complemented
11C11×#1804C212yesmaximal, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C11×#447—24no—
21C2×C11×C4⋊C8C2212yescomplemented
22C2×C11×#102—24no—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2212yescomplemented
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#397—22no—
30C11×#390C2212yes—
31C11×#390C2212yescomplemented
32C11×#386—21no—
33C11×#386—21no—
34C11×#386—22no—
35C11×#382C2212yescomplemented
36C11×#380C2211yescharacteristic
37C11×#379—21no—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yescomplemented
40C11×#340C2212yescomplemented
41C11×#340C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11—21no—
44C22×D4×C11—24no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—42no—
49C22×D4×C11D414yes—
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—22no—
55C23×C4×C11C2311yescharacteristic
56C2×C11×D8—22no—
57C2×C11×D8—22no—
58C2×C11×D8—24no—
59C2×C11×D8—42no—
60C22×C8×C11—22no—
61C22×C8×C11—42no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2312yes—
64C22×C8×C11C2311yescharacteristic
65C11×#121—22no—
66C11×#121—22no—
67C4×D4×C11—24no—
68C4×D4×C11—42no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—44no—
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C42×C11C2312yes—
86C11×C4⋊C8—42no—
87C11×#102—24no—
88C11×#102—24no—
89C11×#102—22no—
90C11×#102—22no—
91C11×#102—42no—
92C11×C22⋊C8—22no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95D412yes—
97#24531C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—24no—
101C24×C11—21no—
102C24×C11—44no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—82no—
106C24×C11C2×D411yescharacteristic
107C2×D4×C11—28no—
108C2×D4×C11—24no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—44no—
119C2×D4×C11—48no—
120C2×D4×C11—44no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11C2×D412yes—
125C2×D4×C11C2×D412yes—
126C2×D4×C11#4114yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—44no—
133C22×C4×C11—44no—
134C22×C4×C11—42no—
135C22×C4×C11—82no—
136C22×C4×C11—82no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C11×D8—44no—
144C11×D8—44no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—44no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—82no—
167C11×C22⋊C4—82no—
168C11×C22⋊C4—82no—
169C42×C11—22no—
170C42×C11—22no—
171C2×#447C2×C1111yescharacteristic
172C22×#102C2×C1111yescharacteristic, complemented
173#2504C2×C1111yescharacteristic, complemented
174D4×C22⋊C4C2×C1111yescharacteristic, complemented
175#2073C2×C1112yescomplemented
176#2054C2×C1112yescomplemented
177#1893C2×C1111yescharacteristic, complemented
178#1879C2×C1112yescomplemented
179#1850C2×C1111yescharacteristic, complemented
180#1824C2×C1111yescharacteristic, complemented
181#1804C2×C1112yescomplemented
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—22no—
187C23×C11—48no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—42no—
195C23×C11—48no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—84no—
202C23×C11—88no—
203C23×C11—88no—
204C23×C11#12112yes—
205C23×C11#13512yes—
206C23×C11AGL(1,ℤ/8)12yes—
207C23×C11C22×D411yescharacteristic
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—24no—
212D4×C11—48no—
213D4×C11—41no—
214D4×C11—41no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—84no—
218D4×C11#12314yes—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—88no—
239C2×C4×C11—84no—
240C2×C4×C11#12112yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4112yes—
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)12yes—
245C8×C11—41no—
246C8×C11—42no—
247C8×C11—41no—
248C23×D4C22×C1111yescharacteristic
249C22×D8C22×C1111yescharacteristic
250C22×D8C22×C1111yescharacteristic
251C23×C8C22×C1111yescharacteristic
252C2×#121C22×C1111yescharacteristic
253C2×C4×D4C22×C1112yes—
254C22×C4⋊C4C22×C1111yescharacteristic
255C22×C22⋊C4—21no—
256#447—24no—
257C2×C4⋊C8C22×C1112yescomplemented
258C2×#102—24no—
259C2×#102C22×C1112yes—
260C2×#102C22×C1111yescharacteristic
261C2×#102C22×C1112yes—
262C2×#102C22×C1111yescharacteristic
263C2×#102C22×C1112yescomplemented
264C2×C22⋊C8C22×C1111yescharacteristic
265#397—22no—
266#390C22×C1112yes—
267#390C22×C1112yescomplemented
268#386—21no—
269#386—21no—
270#386—22no—
271#382C22×C1112yescomplemented
272#380C22×C1111yescharacteristic
273#379—21no—
274C4×C22⋊C4C22×C1111yescharacteristic
275#340C22×C1112yescomplemented
276#340C22×C1112yescomplemented
277#340C22×C1112yescomplemented
278#336C22×C1112yescomplemented
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—816no—
292C22×C11—82no—
293C22×C11—82no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11#46314yes—
300C22×C11C2×#12111yescharacteristic
301C22×C11#54612yes—
302C22×C11C2×#13511yescharacteristic
303C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
304C22×C11#57612yes—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—81no—
309C4×C11—82no—
310C4×C11—82no—
311C4×C11C2×#12311yescharacteristic
312C4×C11#53411yescharacteristic
313C4×C11#55112yes—
314C25—21no—
315C22×D4—24no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—22no—
319C22×D4—42no—
320C22×D4D4×C1114yes—
321C22×D4C23×C1111yescharacteristic
322C22×D4C23×C1111yescharacteristic
323C22×D4C23×C1111yescharacteristic
324C23×C4—21no—
325C23×C4—22no—
326C23×C4C23×C1111yescharacteristic
327C2×D8—22no—
328C2×D8—22no—
329C2×D8—24no—
330C2×D8—42no—
331C22×C8—22no—
332C22×C8—42no—
333C22×C8C23×C1112yes—
334C22×C8C23×C1111yescharacteristic
335C22×C8C23×C1111yescharacteristic
336#121—22no—
337#121—22no—
338C4×D4—24no—
339C4×D4—42no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1112yes—
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4D4×C1111yescharacteristic
355C2×C22⋊C4D4×C1111yescharacteristic
356C2×C42C23×C1112yes—
357C4⋊C8—42no—
358#102—24no—
359#102—24no—
360#102—22no—
361#102—22no—
362#102—42no—
363C22⋊C8—22no—
364#95—21no—
365#95—22no—
366#95—22no—
367#95D4×C1112yes—
368C2×C11—24no—
369C2×C11—44no—
370C2×C11—82no—
371C2×C11—161no—
372C2×C11#241211yescharacteristic
373C2×C11C2×#46311yescharacteristic
374C2×C11#304111yescharacteristic
375C2×C11#329712yes—
376C2×C11#331812yes—
377C24—21no—
378C24—21no—
379C24—24no—
380C24—21no—
381C24—44no—
382C24—42no—
383C24—42no—
384C24—82no—
385C24C2×D4×C1111yescharacteristic
386C2×D4—28no—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—44no—
398C2×D4—48no—
399C2×D4—44no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4C2×D4×C1112yes—
404C2×D4C2×D4×C1112yes—
405C2×D4C11×#4114yes—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—42no—
414C22×C4—82no—
415C22×C4—82no—
416C22×C4C2×D4×C1112yes—
417C22×C4C2×D4×C1112yes—
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1112yes—
420C22×C4C11×#4112yes—
421C22×C4C24×C1111yescharacteristic
422D8—44no—
423D8—44no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—44no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—42no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—44no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—82no—
446C22⋊C4—82no—
447C22⋊C4—82no—
448C42—22no—
449C42—22no—
450C11#2453111yescharacteristic, direct product factor, Sylow
451C23—22no—
452C23—22no—
453C23—22no—
454C23—24no—
455C23—22no—
456C23—48no—
457C23—41no—
458C23—41no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—48no—
465C23—41no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—84no—
471C23—88no—
472C23—88no—
473C23C11×#12112yes—
474C23C11×#13512yes—
475C23C11×AGL(1,ℤ/8)12yes—
476C23C22×D4×C1111yescharacteristic
477D4—22no—
478D4—22no—
479D4—22no—
480D4—24no—
481D4—48no—
482D4—41no—
483D4—41no—
484D4—42no—
485D4—42no—
486D4—84no—
487D4C11×#12314yes—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—88no—
508C2×C4—84no—
509C2×C4C11×#12112yes—
510C2×C4C22×D4×C1111yescharacteristic
511C2×C4C2×C11×#4112yes—
512C2×C4C2×C11×#4111yescharacteristic
513C2×C4C11×H(5,𝔽2)12yes—
514C8—41no—
515C8—42no—
516C8—41no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—24no—
521C22—24no—
522C22—42no—
523C22—42no—
524C22—44no—
525C22—44no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—816no—
530C22—82no—
531C22—82no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—82no—
536C22—82no—
537C22C11×#46314yes—
538C22C2×C11×#12111yescharacteristic
539C22C11×#54612yes—
540C22C2×C11×#13511yescharacteristic
541C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
542C22C11×#57612yes—
543C4—22no—
544C4—42no—
545C4—42no—
546C4—81no—
547C4—82no—
548C4—82no—
549C4C2×C11×#12311yescharacteristic
550C4C11×#53411yescharacteristic
551C4C11×#55112yes—
552C2—24no—
553C2—44no—
554C2—82no—
555C2—161no—
556C2C11×#241211yescharacteristic
557C2C2×C11×#46311yescharacteristic
558C2C11×#304111yescharacteristic
559C2C11×#329712yes—
560C2C11×#331812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C11×#102C2semidirect
3. C11×#2504C2semidirect
4. D4×C11×C22⋊C4C2semidirect
5. C11×#2073C2semidirect
6. C11×#2054C2semidirect
7. C11×#1893C2semidirect
8. C11×#1879C2semidirect
9. C11×#1850C2semidirect
10. C11×#1824C2semidirect
11. C11×#1804C2semidirect
21. C2×C11×C4⋊C8C22semidirect
27. C2×C11×#102C22semidirect
31. C11×#390C22semidirect
35. C11×#382C22semidirect
39. C11×#340C22semidirect
40. C11×#340C22semidirect
41. C11×#340C22semidirect
42. C11×#336C22semidirect
97. #24531C11direct (N × H)
172. C22×#102C2×C11semidirect
173. #2504C2×C11semidirect
174. D4×C22⋊C4C2×C11semidirect
175. #2073C2×C11semidirect
176. #2054C2×C11semidirect
177. #1893C2×C11semidirect
178. #1879C2×C11semidirect
179. #1850C2×C11semidirect
180. #1824C2×C11semidirect
181. #1804C2×C11semidirect
257. C2×C4⋊C8C22×C11semidirect
263. C2×#102C22×C11semidirect
267. #390C22×C11semidirect
271. #382C22×C11semidirect
275. #340C22×C11semidirect
276. #340C22×C11semidirect
277. #340C22×C11semidirect
278. #336C22×C11semidirect
450. C11#24531direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C11×#4472
C22×C11×#1022
C11×#25042
D4×C11×C22⋊C42
C11×#20732
C11×#20542
C11×#18932
C11×#18792
C11×#18502
C11×#18242
C11×#18042
#2453111